Method for noise reduction in images in an image sequence

ABSTRACT

The invention relates to a method for noise suppression in images of an image sequence. 
     It is an object of the invention to find how an iteratively better adapted noise suppression can be ensured for images of an image sequence, in particular given a rising number of images. 
     According to the invention, this object is achieved by a method for noise suppression which provides a low-pass filter algorithm: 
         P   i,j   n+1 =α i,j   n+1   *P   i,j   n +( 1−α   i,j   n+1 )* Q   i,j   n+1  
 
     with an attenuation function α i,j   n+1 =α i,j   n+1 (α0 i,j   n+1 ,Γ i,j   n+1 ).

The invention relates to a method for noise suppression in images of an image sequence.

It is known in the field of digital image processing that characteristic picture disturbances occur in accordance with the properties of the sensors used for image acquisition. Digital images recorded under unfavorable lighting conditions or having a high proportion of dark image areas exhibit a relatively high noise level. Filtering methods which improve the signal-to-noise ratio are generally used in order to reduce the dominating photon noise present in the images. As a rule, for this purpose a time filter is applied to the regions of the images in which no movement is present. A detection of moved image contents is carried out on the basis of the change in intensity determined for each separately considered pixel. It is assumed that a pixel is in movement when the fluctuation in intensity between images of a sequence overshoots a threshold value which is directly related to the standard deviation of the noise. These pixels determined as being in motion are not filtered, or are filtered only slightly. Processing with a rigid recursive time filter as described in patent U.S. Pat. No. 6,314,160 B1, is applied to the pixels determined as static or immobile. The use of a recursive low-pass as a filter base limits the maximum averaging length over an image sequence. The method therefore has a limited quality of noise suppression and a slow transient response.

It is an object of the invention to find how an iteratively better adapted noise suppression can be ensured for images of an image sequence, in particular given a rising number of images.

This object is achieved according to the invention by a method for noise suppression which provides a low-pass filter algorithm:

P _(i,j) ^(n+1)=α_(i,j) ^(n+1) *P _(i,j) ^(n)+(1−α_(i,j) ^(n+1))*Q _(i,j) ^(n+1)

with an attenuation function α_(i,j) ^(n+1)=α_(i,j) ^(n+1)(α0_(i,j) ^(n+1),Γ_(i,j) ^(n+1)). For each pixel, the attenuation function α_(i,j) ^(n+1) is dependent, firstly, on an attenuation factor α0_(i,j) ^(n+1) and, secondly, on a movement measure Γ_(i,j) ^(n+1). The movement measure Γ_(i,j) ^(n+1) is dependent on a grayscale value difference dQ_(i,j) ^(n+1)=|P_(i,j) ^(n)−Q_(i,j) ^(n+1)| between filtered and unfiltered pixel, a prescribable difference threshold dif_swl, and on an amplitude of the grayscale value Q_(i,j) ^(n+1) of the pixel.

The attenuation factor α0_(i,j) ^(n+1) is adapted to the duration of the immobility Γ_(i,j) ^(n+1)≈0 of the grayscale value of a pixel. Furthermore, a lower limiting value α0_(min) and an upper limiting value α0_(max) are defined for the attenuation factor α0_(i,j) ^(n+1). In addition, the recursive filtering of unmoved pixels (Γ_(i,j) ^(n+1)≈0) has an attenuation factor approaching α0_(max), and the recursive filtering of moved pixels (Γ_(i,j) ^(n+1)≈1) with high grayscale value dynamics has an attenuation factor approaching α0_(min).

The invention is to be explained in more detail below with the aid of exemplary embodiments.

In one variant of the method, a filter algorithm with a recursive averaging is applied to each pixel of an image from a sequence. The low-pass filter used for this purpose acts iteratively with an attenuation function α_(i,j) ^(n+1), adapted for the pixel, on the grayscale value difference dQ_(i,j) ^(n+1) from the grayscale value Q_(i,j) ^(n+1) of the pixel of a currently recorded image and the grayscale value P_(i,j) ^(n) of the pixel of a previously recorded and already filtered image. The attenuation function acts in dependence on an attenuation factor α0_(i,j) ^(n+1) adapted for the pixel, and the movement measure Γ_(i,j) ^(n+1).The value of the movement measure Γ_(i,j) ^(n+1) is governed by the grayscale value difference dQ_(i,j) ^(n+1) and is influenced by a threshold value dif_swl to be prescribed, and a weighting factor γ_(i,j) ^(n+1). This weighting factor γ_(i,j) ^(n+1) is dependent on the grayscale value αQ_(i,j) ^(n+1) and a reference grayscale value Q0. The adaptation of the attenuation factor α0_(i,j) ^(n+1) is likewise performed as a function of the movement measure Γ_(i,j) ^(n+1) and the value of the already iterativeiy adapted attenuation factor α0_(i,j) ^(n), which was used to filter the previous image.

The invention is based on the finding that moved image contents can be detected when the grayscale value of the dynamic image contents stands out from the grayscale value of the static image contents. The difference thus produced is therefore higher than the difference which occurs between noisy pixels in a static image section. This distinction can be used to process dynamic image contents with a different noise suppression than the static ones. The inventive filter algorithm can be used for iterativeiy amplifying the attenuating filter action in noisy, static image areas and reducing it in dynamic image areas or for admitting no attenuation at all.

The decision as to whether a pixel is to be classified as dynamic or static is performed using the movement measure Γ_(i,j) ^(n+1). It is defined by:

$\Gamma_{i,j}^{n + 1}\left\{ \begin{matrix} {= {\frac{Q_{i,j}^{n + 1}}{dif\_ swl}*\gamma_{i,j}^{n + 1}}} & \left\lbrack {{{for}\mspace{14mu} {Q_{i,j}^{n + 1}}*\gamma_{i,j}^{n + 1}} < {dif\_ swl}} \right\rbrack \\ {= 1} & \lbrack{otherwise}\rbrack \end{matrix} \right.$

The threshold value dif_swl and the weighting factor γ_(i,j) ^(n+1) are used to weight the grayscale value difference dQ_(i,j) ^(n+1). The threshold value dif_swl is prescribed, and the weighting factor γ_(i,j) ^(n+1) is calculated as follows:

$\gamma_{i,j}^{n + 1}\left\{ \begin{matrix} {= \sqrt{\frac{Q\; 0}{Q_{i,j}^{n + 1}}}} & \left\lbrack {{{for}\mspace{14mu} Q_{i,j}^{n + 1}} > {Q\; 0}} \right\rbrack \\ {= 1} & \left\lbrack {{for}\mspace{14mu} {otherwise}} \right\rbrack \end{matrix} \right.$

The noise of a pixel is dependent on the signal strength of its grayscale value. Lighter pixels have a stronger noise performance than darker ones do. Consequently, the brightness of the grayscale value of a pixel is taken into account by the use of the reference grayscale value Q0. An advantageous value of Q0 is at 30% of the maximum grayscale value GW_(max). The threshold value dif_swl can assume values between 0 and GW_(max), and determines the separation between moved and unmoved pixels. The value of this threshold value dif_swl therefore influences the strength of the edge smearing on moved image contents.

The attenuation function α_(i,j) ^(n+1) is dependent substantially on the grayscale value difference dQ_(i,j) ^(n+1), the signal strength Q_(i,j) ^(n+1) and the attenuation factor α0_(i,j) ^(n+1):

${\alpha_{i,j}^{n + 1} = {\alpha \; 0_{i,j}^{n + 1}*\left( {1 - \Gamma_{i,j}^{n + 1}} \right)}},{{where}\text{:}\mspace{14mu} \Gamma_{i,j}^{n + 1}\left\{ {{\begin{matrix} {= \frac{{\overset{\sim}{Q}}_{i,j}^{n + 1}}{dif\_ swl}} & \left\lbrack {{{for}\mspace{14mu} {{\overset{\sim}{Q}}_{i,j}^{n + 1}}} < {dif\_ swl}} \right\rbrack \\ {= 1} & \left\lbrack {{for}\mspace{14mu} {otherwise}} \right\rbrack \end{matrix}{where}\text{:}\mspace{14mu} {{\overset{\sim}{Q}}_{i,j}^{n + 1}}} = {{Q_{i,j}^{n + 1}}*\gamma_{i,j}^{n + 1}}} \right.}$

An iterative adaptation of the attenuation factor α0_(i,j) ^(n+1) in the direction of a stronger attenuation effect over the duration of the immobility P_(i,j) ^(n+1)≈P_(i,j) ^(n) of a pixel Q_(i,j) ^(n+1) leads to an improved noise suppression. In the case of unmoved pixels, an advantageous adaptation of the attenuation factor is given by the following sequence:

α0={½, ⅔, ¾, ⅘, ⅚, 6/7, . . . }

Given lasting immobility, the attenuation factor α0_(i,j) ^(n+1) is increased iteratively, and so it approaches the value 1, and the attenuation function α_(i,j) ^(n+1) therefore enables a maximum noise suppression at this pixel.

The attenuation factor α0_(i,j) ^(n+1) is therefore dependent on the attenuation factor α0_(i,j) ^(n), which was used to filter the pixel of the previous image, and on the movement measure Γ_(i,j) ^(n+1) of a pixel of the current image. It is evident that the attenuation factor α0_(i,j) ^(n+1) is increased for a small movement measure Γ_(i,j) ^(n+1), and reduced for a large movement measure Γ_(i,j) ^(n+1). This is performed within the prescribed limiting values α0_(min) and α0_(max). An advantageous implementation of this adaptation can be performed in this defined subdivision:

$\alpha \; 0_{i,j}^{n + 1}\left\{ \begin{matrix} {= {{\alpha 0}_{i,j}^{n} + \Delta_{\alpha}}} & \left\lbrack {{{for}\mspace{14mu} 0} \leq \Gamma_{i,j}^{n + 1} \leq {1/3}} \right\rbrack \\ {= {\alpha 0}_{i,j}^{n}} & \left\lbrack {{{for}\mspace{14mu} {1/3}} \leq \Gamma_{i,j}^{n + 1} \leq {2/3}} \right\rbrack \\ {= {{\alpha 0}_{i,j}^{n} - \Delta_{\alpha}}} & \left\lbrack {{{for}\mspace{14mu} {2/3}} \leq \Gamma_{i,j}^{n + 1} < 1} \right\rbrack \\ {= {\alpha 0}_{\min}} & \left\lbrack {{{for}\mspace{14mu} \Gamma_{i,j}^{n + 1}} = 1.0} \right\rbrack \end{matrix} \right.$

The following adaptation resulting from threshold value overshooting:

${\alpha 0}_{i,j}^{n + 1}\left\{ \begin{matrix} {= {\alpha 0}_{\min}} & \left\lbrack {{{for}\mspace{14mu} \alpha_{i,j}^{n + 1}} < {\alpha 0}_{\min}} \right\rbrack \\ {= {\alpha 0}_{\max}} & \left\lbrack {{{for}\mspace{14mu} \alpha_{i,j}^{n + 1}} > {\alpha 0}_{\max}} \right\rbrack \\ {= {\alpha 0}_{i,j}^{n + 1}} & {\left\lbrack {{for}\mspace{14mu} {otherwise}} \right\rbrack.} \end{matrix} \right.$

If a pixel is classified as not moved or as noisy, the attenuation factor from the preceding filter pass is increased by the absolute value Δ_(α), and so the attenuation is increased. In the case of a pixel classified only as moderately moved, the attenuation factor α0_(i,j) ^(n+1) is adopted without change. If the pixel is classified as moved, the damping factor α0_(i,j) ^(n) from the previous filter pass is attenuated by the absolute value Δ_(α). A pixel classified as strong in movement resets the filter strength of the attenuation factor α0_(i,j) ^(n+1) to the lower limiting value α0_(min), as a result of which only very slight attenuation, or no further attenuation takes place at this pixel.

If the adaptation of the attenuation factor α0_(i,j) ^(n+1) is to be done yet more variably and exactly, it is advantageous to store a more comprehensive differentiating subdivision of ranges in a look-up table.

SYMBOLS

α0—sequence of attenuation factors

α0_(max)/α0_(min)—upper/lower limiting value of the attenuation factor

α0_(i,j) ^(n+1)—attenuation factor adapted to pixel

α0_(i,j) ^(n)—attenuation factor of the predecessor

α_(i,j) ^(n+1)—attenuation function adapted to the pixel

α_(i,j) ^(n)—attenuation function that was applied to the predecessor

Δ_(α)—absolute value of the change in the attenuation factor

Q0—reference grayscale value

GW_(max)—maximum grayscale value

Q_(i,j) ^(n+1)—grayscale value of the current pixel

dQ_(i,j) ^(n+1)—grayscale value difference from P_(i,j) ^(n) and Q_(i,j) ^(n+1)

P_(i,j) ^(n+1)—grayscale value of the current pixel after fiItering

P_(i,j) ^(n)—grayscale value of the preceding pixel after filtering

dif_swl—threshold value for movement measure

γ_(i,j) ^(n+1)—weighting factor (grayscale value)

Γ_(i,j) ^(n+1)—movement measure 

1. A method for noise suppression in images of an image sequence in accordance with the following algorithm: P _(i,j) ^(n+1)=α_(i,j) ^(n+1) *P _(i,j) ^(n)+(1−α_(i,j) ^(n+1))*Q _(i,j) ^(n+1) where: P_(i,j) ^(n+1)=grayscale value of a pixel of the ith row and the jth column after the (n+1)th iteration, P_(i,j) ^(n)=grayscale value of a pixel of the ith row and the jth column after the (n)th iteration, Q_(i,j) ^(n+1)=grayscale value of a pixel of the ith row and the jth column after the (n+1)th recording (unfiltered), and d_(i,j) ^(n+1)=attenuation function for a pixel in the ith row and the jth column, the algorithm being a recursive law-pass with an attenuation function α_(i,j) ^(n+1) adapted for the pixel, and the action of the attenuation being dependent on a grayscale value difference dQ_(i,j) ^(n+1)=|P_(i,j) ^(n)−Q_(i,j) ^(n+1)| between. filtered and unfiltered pixels, on an amplitude of the grayscale value Q_(i,j) ^(n+1) of the pixel, it further being the case that: $\gamma_{i,j}^{n + 1}\left\{ \begin{matrix} {= \sqrt{\frac{Q\; 0}{Q_{i,j}^{n + 1}}}} & \left\lbrack {{{for}\mspace{14mu} Q_{i,j}^{n + 1}} > {Q\; 0}} \right\rbrack \\ {= 1} & \left\lbrack {{for}\mspace{14mu} {otherwise}} \right\rbrack \end{matrix} \right.$ where γ_(i,j) ^(n+1)=weighting factor, and Q0—reference grayscale value, characterised in that an adaptation of the strength of the attenuation factor α0_(i,j) ^(n+1) is performed taking account of the sequence length in which a pixel of the ith row and the jth column has an unchanged grayscale value, the attenuation factors α0_(i,j) ^(n+1) with a limiting value α0_(min) and a limiting value α0_(max) are defined, a movement measure $\Gamma_{i,j}^{n + 1}\left\{ \begin{matrix} {= {\frac{Q_{i,j}^{n + 1}}{dif\_ swl}*\gamma_{i,j}^{n + 1}}} & \left\lbrack {{{for}\mspace{14mu} {Q_{i,j}^{n + 1}}*\gamma_{i,j}^{n + 1}} < {dif\_ swl}} \right\rbrack \\ {= 1} & \lbrack{otherwise}\rbrack \end{matrix} \right.$ is set up as a function of a threshold value dif_swl, it then being the case that: α_(i,j) ^(n+1)=α0_(i,j) ^(n+1)*(1−Γ_(i,j) ^(n+1)), a weighting of the attenuation factor α0_(i,j) ^(n+1) is performed as a function of the movement measure Γ_(i,j) ^(n+1), the recursive filtering of unmoved pixels with an attenuation factor α0_(i,j) ^(n+1) approaching α0_(max) is performed, and the recursive filtering of moved pixels with an attenuation factor α0_(i,j) ^(n+1) approaching α0_(min) is performed. 